#include <algorithm>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <string>
#include <list>
#include <bitset>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <cmath>
#include <cassert>
#include <ctime>
#include <numeric>
#include <functional>
#include <valarray>
#include <complex>
#include <utility>
using namespace std;

const int dx[]={0,-1,0,1,-1,1, 1,-1};
const int dy[]={1,0,-1,0, 1,1,-1,-1};
const double eps=1e-8;

typedef long long LL;
typedef unsigned long long uLL;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vgraph;
typedef vector<pii> vpii;
typedef vector<LL> vLL;
typedef vector<string> vs;

#define sz(a) (int)a.size()
#define fori(i,a,b) for(int i(a),_b(b);i<=_b;++i)
#define ford(i,a,b) for(int i(a),_b(b);i>=_b;--i)
#define forn(i,n) fori(i,0,n-1)
#define fora(i,a) forn(i,sz(a))
#define fore(it,c) for(typeof((c).begin()) it=(c).begin();it!=(c).end();++it)
#define all(a) a.begin(),a.end()
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define clear0(a) memset(a,0,sizeof(a))
#define clearm1(a) memset(a,-1,sizeof(a))
#define maximum(a) (*max_element(all(a)))
#define minimum(a) (*min_element(all(a)))
#define findx(a,x) (find(all(a),x)-a.begin())
#define two(X) (1LL<<(X))
#define contain(S,X) ((S)&two(X))
#define setbit(S,X) ((S)|=two(X))
#define clearbit(S,X) ((S)&=~two(X))
#define togglebit(S,X) ((S)^=two(X))
#define sqr(a) ((a)*(a))
#define finp "input.inp"
#define fout "output.out"
#define nmax 100
#define mmax 100
#define kmax 10
#define modulo 1000000007
#define maxc 999999999

#define debugprint(a) cout << a << ' '
template <typename T>
void debugprintarr(T arr,int x, int y)
{
    fori(i,x,y) debugprint(arr[i]);
    cout << '\n';
}

template <typename T>
void debugprint2darr(T arr, int x1, int y1, int x2, int y2)
{
    fori(i,x1,y1) debugprintarr(arr[i],x2,y2);
}

int main()
{
	#ifndef ONLINE_JUDGE
		freopen(finp,"r",stdin);
		freopen(fout,"w", stdout);
	#endif
	return 0;
}
